Sheila departed from her family's residence on Plyers Mill Road in Kensington, Maryland on March 25, 1975 with her younger sister, Katherine Lyon, between 11:00 a.m. and 12:00 p.m. The girls were walking to the Wheaton Plaza Shopping Center in Wheaton, Maryland, which was approximately one-half mile from their home and located on the corner of University Boulevard and Veirs Mills Road. It was the first day of Easter vacation from school and Katherine and Sheila wanted to see the Easter exhibits at the mall, as well as have a pizza lunch at The Orange Bowl Restaurant.

A neighborhood child saw the girls outside the restaurant at approximately 1:00 p.m. He told investigators that the sisters were speaking to an unidentified middle-aged man, 50 to 60 years old, who was wearing a brown suit. The man was carrying a briefcase with a tape recorder inside; there were also other children around who were speaking into a microphone he was holding. Two composite sketches of the man were created, and several individuals recognized him; they reported seeing him at the Marlow Heights Shopping Center and the Iverson Mall both in Prince George's County, Maryland. He approached several young girls and asked them to read read an answering machine message typed on an index card into his hand held-microphone. He has never been identified. Later, investigators concluded the individual had not been involved in the girls' disappearances.

The girls' fifteen-year-old brother saw them inside The Orange Bowl Restaurant eating pizza together at approximately 2:00 p.m. the day they vanished. A friend stated that the girls were walking westward down Drumm Avenue near Devon Street between 2:30 and 3:30 p.m. This would have been one of the most direct routes to their home on Plyers Mill Road from the mall and was the final confirmed sighting of the sisters. Their mother had instructed Sheila and Katherine to return to the residence by 4:00 p.m. When they did not arrive by 7:00 p.m. authorities were summoned and an extensive search was conducted. No evidence of the Lyon sisters' whereabouts could be located.

Several extortion-type phone calls were made to the Lyon family in the weeks following the girls' disappearances. The most serious call came from an unidentified male on April 4, 1975. The individual demanded that their father leave a briefcase with $10,000 inside an Annapolis, Maryland courthouse restroom. The money was left as per the instructions but was never claimed. The caller later maintained that police had surrounded the courthouse and he could not retrieve the ransom. Before the money would be offered to the man again, he was required to show evidence of the Lyon sisters in his custody. The caller said he would be in touch with the family, but never called back.

A witness in Manassas, Virginia reported seeing two girls resembling Sheila and Katherine in the rear of a beige 1968 Ford station wagon on April 7, 1975. The witness stated that the girls were observed bound and gagged in the vehicle at approximately 7:30 a.m. that day. The driver of the station wagon resembled the man seen questioning children at The Orange Bowl Restaurant the day the sisters vanished. When the driver spotted the witness tailing him, he ran a red light and sped west on Route 234 towards Interstate 66 in Virginia. The station wagon had Maryland license plates with the possible combination "DMT-6**." The last two numbers are unknown due to the bending of the car's plate. The known combination was issued in Cumberland, Hagerstown and Baltimore, Maryland at the time. A search for matching plate numbers failed to produce any information. This witness's report was at first treated as credible, but was later deemed "questionable" by police.

In 2014, authorities named Lloyd Lee Michael Welch Jr. and Richard Allen Welch, Sr. as the prime suspects in the sisters' cases. Lloyd, who is also known as Michael Lee Welch, is Richard's nephew. He was 18 years old in 1975. Photos of the men, both of whom are still alive, are posted below this case summary. Lloyd has a record numerous criminal offenses, includng sex offenses against young girls in South Carolina, Virginia and Delaware. Since 1997 he's been serving a 30-year sentence in a Delaware prison. He traveled throughout the United States from the 1970s to the 1990s and worked for a traveling carnival. He was at the Wheaton Plaza Shopping Center the day Katherine and Sheila went missing, and was observed watching them. Investigators believe Richard worked as a security guard at the area.

Lloyd told authorities he'd left the mall with Katherine and Sheila the day of their disappearances, and later saw his uncle sexually assaulting one of the them. He said he left the residence and never saw either of the children again. Investigators believe the girls' remains may be buried on Taylors Mountain about 200 miles from their home; Richard apparently owned property there in the 1970s, and so did his sister. A grand jury investigation into the children's disappearances began in 2014. Richard's wife testified, and authorities believe she lied on the stand; she was subsequently charged with perjury.

In July 2015, a grand jury indicted Lloyd for first-degree felony murder in Sheila and Katherine's cases; the felony was abduction with intent to defile. He faces 20 years to life in prison, or possibly the death penalty, if convicted. Authorities stated there was a "conspiracy" involved in the Lyon sisters' presumed deaths and it was possible more arrests would be made and indictments issued.

Active searches for the Lyon sisters' bodies commenced in 2014. Foul play is suspected in their cases due to the circumstances involved.